Looking for a simple method to combine hard + 0 jet and hard + 1 jet - PowerPoint PPT Presentation

Looking for a simple method to combine “hard + 0 jet” and “hard + 1 jet” event generators Shigeru ODAKA Institute of Particle and Nuclear Studies High Energy Accelerator Research Organization (KEK) shigeru.odaka@kek.jp

Motivation • There are many needs to simulate “ hard interaction + 1 or 2 jet ” processes in hadron collisions, in order to estimate backgrounds and, sometimes, signals. • We have many “hard + 1 jet” generators, but encounter an apparent double-count problem . • A “hard + 0 jet” generator + PS would give us a better description for relatively soft jets; “hard +1 jet” generators should be used for hard jets. • There must be a consistent way to merge them . • There are some theoretically clear methods: ME corrections in PYTHIA and HERWIG, LL-subtraction in the NLO calculation by Kurihara et al. They are process-dependent. Is there any process-independent way?. • The CKKW method may be a solution, but there must be a simpler way because we need only 1 or 2 jets. • I started an exploration from the simplest case: “ W + 0 jet” and “ W + 1 jet”.

Double count in “hard + 1 jet” • Two energy scales in ME : a “hard” process scale and a cut for the jet. 2 (factorization scale) = < m T – Usually, we take µ F 2 > = m W 2 /2 + 2 (ME) (> p T 2 (ME jet) ) for “ W + 1 jet”. p T PDF or PS is a jet-radiation correction up to Q (jet) ( ≈ p T (jet)) = µ F . • • There is an apparent overlap in the phase space; i.e . a double count. – It may happen that p T (ME jet) < p T (PS jet). We must constrain Q (ME jet) > µ F . This preserves a virtuality ordering.

Double count between “hard + 0 jet” and “hard + 1 jet” Usually, we take µ F = m W in “ W + 0 jet”. • • If we take p T ,min (ME jet) < m W in “ W + 1 jet”, there is an overlap in the “jet” phase space; another double count. We have to use a common µ F in “hard + 0 jet” and “hard + 1 jet”. – It should be considered as a boundary between the corrections by PDF/PS and ME.

Where should we place µ F ? µ F = “hard” energy scale would be the maximum. • • It must be in a region where both the ME and the collinear approximation of PDF/PS work well. • It should not be very small. – If very small, double-scale effects would become large, i.e. , α s ( Q 2 ) and Sudakov-factor corrections would become necessary, just like the CKKW method.

The 1st try using PYTHIA 6.2 Setup • LHC condition • MSEL = 12 without ME correction for “ W + 0 jet” 2 = (default); no other choice is allowed. µ F ˆ – s • MSEL = 14 for “ W + 1 jet” 2 required. – Q 2 (ME jet) ≡ min{| t |, | u |} > µ F 2 = < m T µ F 2 > (default) – This is not ideal but most of the double counts are avoided because of the Q (ME jet) cut. • MSEL = 12 with ME corr. (default) is a good reference for the tests. • Only the initial-state PS is turned on.

The 1st try using PYTHIA 6.2 Result • A good shape in p T ( W ) > m W , where “ W + 1 jet” covers. • But a deficit below m W where “ W + 0 jet” should dominate. – An ambiguity in the Q (ME jet) definition ( t - u mix) and a contribution of an s -channel process might be the reason; i.e ., PS does not simulate u - and s -channel contributions. • These effects (over-rejection in ME or deficit in PS) will be reduced if µ F is set smaller.

Tests using GR@PPA_All (PYTHIA6.2-embed) Setup • LHC condition • ISUB = 421 for “ W + 0 jet” • ISUB = 422, 423 for “ W + 1 jet” – Q 2 (ME jet) ≡ min{| t |, | u |} > µ F 2 required µ R (renormalisation scale) = p T (ME jet): not important now. – Common µ F (= µ PS ) • – It is passed to PYTHIA via the “energy scale” parameter in the Les Houches external generator interface, to be used as the PS energy-scale. W → e ν decay only. • • Only the initial-state PS is turned on. – “jet = parton” assumed. Tests for µ F = ˆ ˆ • ( W ) and ( W ) /2 s s

“ W + 0 jet” µ F = µ PS = F × ˆ ( W ) s F = 1.0 0.5 0.2 0.1

“ W + 0 jet” F = 1.0 0.5 0.2 0.1

“ W + 0 jet” F = 1.0 0.5 0.2 0.1

| η | < 4.5

| η | < 4.5

Tests using GR@PPA_All (PYTHIA6.2-embed) Result • Similar to the PYTHIA result when µ F = . ˆ ( W ) s • The deficit below µ F still exists even if µ F = . ˆ ( W ) /2 s • Only 1% change in the total cross section. • Very bad connection in the p t (max- p t jet) distribution. • “W + 0 jet” looks too soft; especially, the “jet” p t . – Well known fact? – Any simple solution?

Summary • A very naïve method based on a reconsideration of double- count problems does not show a good result. • If no simple solution, – I answer to my colleagues “Wait for the CKKW!”, and go to a generalization of the LL-subtraction method.